Question: The grades on a math midterm at Springer are normally distributed with $\mu = 83$ and $\sigma = 4.0$. Stephanie earned a n $84$ on the exam. Find the z-score for Stephanie's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Stephanie's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{84 - {83}}{{4.0}}} $ ${ z \approx 0.25}$ The z-score is $0.25$. In other words, Stephanie's score was $0.25$ standard deviations above the mean.